A tape dispenser holds 1.14 x 10^4 mm of tape that is 12.7 mm wide. Multiply the two numbers to find the total area in square millimeters of tape. Write the product in scientific notation.

Question

answers:

1.4478 x 10^5 mm^2

14.478 x 10^5 mm^2

1.4478 x 10^4 mm^2

14.478 x 10^4 mm^2

Answer 1

To find the total area of the tape in square millimeters, we need to multiply the length of the tape by its width.

Given:

• Length of tape = \(1.14 \times 10^4\) mm
• Width of tape = 12.7 mm

Now, multiply these two values:

\[ \text{Area} = 1.14 \times 10^4 \text{ mm} \times 12.7 \text{ mm} \]

First, calculate \(1.14 \times 12.7\):

\[ 1.14 \times 12.7 = 14.478 \]

Next, we can combine this with the power of ten:

\[ \text{Area} = 14.478 \times 10^4 \text{ mm}^2 \]

Since scientific notation typically has a single non-zero digit to the left of the decimal, we should convert \(14.478\) to scientific notation:

\[ 14.478 = 1.4478 \times 10^1 \]

So we adjust the area accordingly:

\[ \text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} \text{ mm}^2 \]

Therefore, the total area in scientific notation is: \[ \boxed{1.4478 \times 10^5 \text{ mm}^2} \]

Answer 2

are you sure

Answer 3

Let’s verify the calculation step-by-step to ensure accuracy:

1. Length of tape: \( 1.14 \times 10^4 \) mm
2. Width of tape: \( 12.7 \) mm

Now, we multiply these two values to find the area:

\[ \text{Area} = \text{Length} \times \text{Width} = (1.14 \times 10^4) \times 12.7 \]

3. Calculate \( 1.14 \times 12.7 \):

\[ 1.14 \times 12.7 = 14.478 \]

4. Combine with the scientific notation for length:

The length is in scientific notation, so:

\[ \text{Area} = 14.478 \times 10^4 \text{ mm}^2 \]

5. Convert \( 14.478 \) into scientific notation:

To convert \( 14.478 \) into scientific notation, we express it as:

\[ 14.478 = 1.4478 \times 10^1 \]

6. Combine it with \( 10^4 \):

\[ \text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} \text{ mm}^2 \]

The calculation and conversion were executed correctly, confirming that the total area of tape is:

\[ \boxed{1.4478 \times 10^5 \text{ mm}^2} \]

So, yes, the answer is indeed accurate. Thank you for prompting this verification!